Original Article Dynamics of nonlinearly damped microcantilevers under electrostatic excitation S Chaterjee 1 and G Pohit 2 Abstract Nonlinear dynamic behaviour of a cantilever microbeam actuated by a combination of DC and AC loading are investigated in presence of squeeze-film damping. A reduced order model formulated accounting for the nonlinearities of the system arising out of electrostatic forces and squeeze-film damping is numerically simulated to observe the large amplitude dynamic characteristics near primary and superharmonic resonances. The emphasis is on the significance of nonlinear damping in capturing the true dynamic characteristics of microsystems formulated as distributed parameter model. The damping nonlinearity is found to considerably affect the dynamics with a profound stabilising effect on the microsystem. Under the effect of large DC bias voltage, frequency–response curves obtained for different amplitudes of AC excitation exhibit local and global bifurcations. Response sensitivity to initial conditions is investigated near bifurcation points. Findings in the superharmonic resonance domain are emphasised. Keywords Microelectromechanical systems, squeeze-film damping, bifurcation, nonlinear resonance, dynamic pull-in Date received: 20 July 2012; accepted: 21 September 2012 Introduction Due to the nonlinear nature of the electrostatic forces, microelectromechanical systems (MEMS) gives rise to interesting nonlinear phenomenon that can have sig- nificant impact in their applications as capacitive switches, resonators and micromirrors. Moreover, the damping of electrically actuated microstructures vibrating in presence of fluid trapped in the narrow gap between deformable and fixed electrodes is domi- nated by nonlinear squeeze-film damping. 1 There has been much research work undertaken to address the manifestations of these nonlinearities. In McCarthy et al. 2 and Krylov and Maimon, 3 dynamic pull-in instabilities were investigated for purely DC loads under damped operating conditions. Purely DC loads and undamped operating conditions were dealt in Chaterjee and Pohit. 4 Dynamic charac- teristics of microstructures under combined DC and AC loading differ from those under purely DC loads. De and Aluru 5 investigated the effects of electrostatic, mechanical, and fluidic nonlinearities on microstruc- tures. Full Lagrangian-based relaxation and Newton schemes were presented to simulate period doubling route to chaos under superharmonic excitations. Alsaleem et al. 6 conducted experiment on a microcan- tilever attached to a proof mass at its end under low pressure and revealed large primary and subharmonic deflections with softening behaviour. Nayfeh and Younis 7 studied a linearly damped clamped–clamped beam microresonator using a combination of a shoot- ing technique and a reduced order model (ROM). The dynamics of a doubly clamped microbeam for vari- ations in initial conditions were studied 8 using long- time integration technique. Mestrom et al. 9 compared the experimental observations of a doubly clamped beam microresonator with the numerically simulated results. The frequency response curves revealed sub- harmonic resonance of order one-half preceded by period doubling bifurcation of period two. Harish et al. 10 used a lumped model of a micro-ring resonator to show jump phenomenon at high values of paramet- ric excitation. Zhu et al. 11 studied the nonlinear coupling effect between the adjacent microbeams of a large array of interacting microcantilevers. Analysis 1 Department of Mechanical Engineering, C V Raman College of Engineering, Bhubaneswar, India 2 Department of Mechanical Engineering, Jadavpur University, Kolkata, India Corresponding author: S Chaterjee, Department of Mechanical Engineering, C V Raman College of Engineering, Bhubaneswar 752054, India. Email: jeesaikat@gmail.com Proc IMechE Part C: J Mechanical Engineering Science 227(3) 630–646 ! IMechE 2012 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0954406212465371 pic.sagepub.com